Nonlinear subspace clustering by functional link neural networks

The functional link neural network (FLNN) increases the input dimension by functionally expanding the input features. In this paper, modifications to the FLNN are proposed for undertaking data classification tasks. The main objective is to optimize the FLNN by formulating a parsimonious network with less complexity and lower computational burden as compared with the original FLNN. The methodology consists of selecting a number of important expanded features to build the FLNN structure. It is based on the rationale that not all the expanded features are equally important in distinguishing different target classes. As such, we modify the FLNN in a way that less—relevant and redundant expanded input features are identified and discarded. In addition, instead of using the back-propagation learning algorithm, adjustment of the network weights is formulated as an optimisation task. Specifically, the genetic algorithm is used for both feature selection as well as weight tuning in the FLNN. An experimental study using benchmark problems is conducted to evaluate the efficacy of the modified FLNN. The empirical results indicate that even though the structure of the modified FLNN is simpler, it is able to achieve comparable classification results as those from the original FLNN with fully expanded input features.

In this chapter, the primary focus is on theoretical and empirical study of functional link neural networks (FLNNs) for classification. We present a hybrid Chebyshev functional link neural network (cFLNN) without hidden layer with evolvable particle swarm optimization (ePSO) for classification. The resulted classifier is then used for assigning proper class label to an unknown sample. The hybrid cFLNN is a type of feed-forward neural networks, which have the ability to transform the non-linear input space into higher dimensional space where linear separability is possible. In particular, the proposed hybrid cFLNN combines the best attribute of evolvable particle swarm optimization (ePSO), back-propagation learning (BP-Learning), and Chebyshev functional link neural networks (CFLNN). We have shown its effectiveness of classifying the unknown pattern using the datasets obtained from UCI repository. The computational results are then compared with other higher order neural networks (HONNs) like functional link neural network with a generic basis functions, Pi-Sigma neural network (PSNN), radial basis function neural network (RBFNN), and ridge polynomial neural network (RPNN).

Functional Link Neural Network (FLNN) has becoming as an important tool used in machine learning due to its modest architecture. FLNN requires less tunable weights for training as compared to the standard multilayer feed forward network such as Multilayer Perceptron (MLP). Since FLNN uses Backpropagation algorithm as the standard learning algorithm, the method however prone to get trapped in local minima which affect its performance. This paper proposed the implementation of Ant Lion Algorithm as learning algorithm to train the FLNN for classification tasks. The Ant Lion Optimizer (ALO) is the metaheuristic optimization algorithm that mimics the hunting mechanism of antlions in nature. The result of the classification made by FLNN-ALO is compared with the standard FLNN model to examine whether the ALO learning algorithm is capable of training the FLNN network and improve its performance. From the result achieved, it can be seen that the implementation of the proposed learning algorithm for FLNN performs the classification task quite well and yields better accuracy on the unseen data.

Functional Link Neural Network (FLNN) has become as an important tool used in classification tasks due to its modest architecture. FLNN requires less tunable weights for training as compared to the standard multilayer feed forward network. Since FLNN uses Backpropagation algorithm as the standard learning scheme, the method however prone to get trapped in local minima which affect its classification performance. This paper proposed the implementation of modified Bee-Firefly algorithm as an alternative learning scheme for FLNN for the task of mammographic mass classification. The implementation of the proposed learning scheme demonstrated that the FLNN can successfully perform the classification task with better accuracy result on unseen data.

This paper presents the prediction of financial time series using an adaptive neural network, which is called the self-organised multilayer perceptrons inspired by the immune algorithm. The simulation results were compared with the multilayer perceptrons and the functional link neural networks. The prediction capability of the various neural networks was tested on ten different data sets; the US/UK exchange rates, the JP/US exchange rate, the US/EU exchange rates, NASDAQO time series, NASDAQC time series, DJIAO time series, DJIAC time series, DJUAO time series, DJUAC time series and the oil price. We carried out two sets of experiments. In the first set, the input data are pre-processed between 0 and 1 and passed to the neural networks as non-stationary data. In the second set of experiments, the non-stationary input signals are transformed into stationary signals and passed to the neural networks. The predictions demonstrated that all neural networks generate profit using stationary data and fail to generate any profit when using non-stationary data. Furthermore, the experiment results for the stationary signals showed that the (SOMLP) outperforms the MLP neural network based on the profit. However, it produced a lower profit when predicting stock price in comparison with the Functional Link neural networks.

The artificial neural network has been proved among the best tools in data mining for classification tasks. The concept of obtaining more accurate classifier with less computational complexity has been gaining importance, because of day by day increase in the data. Several numbers of models have been developed for classification problems. This paper is the depiction of higher order neural networks especially Fibonacci Functional Link Neural Network (FFLNN) for data classification. The coefficients of individual terms in Fibonacci polynomials are smaller than those of individual terms in the classical orthogonal polynomials. Additionally, less number of terms make it a preferable classifier regarding functional expansion. These properties lead this FFLNN to produce more accurate higher order neural network with less computational complexity to tackle the classification problems. Four datasets were collected from KEEL and LIBSVM dataset repositories. Computational results were compared with three benchmarked models including Chebyshev Functional Link Neural Network (CFLNN), Chebyshev Multilayer Perceptron (CMLP) and Multilayer Perceptron Neural Network (MLP). A t-test was applied to check the significance of the proposed classifier based on classification performance. The findings showed that the proposed classifier outperformed all benchmarked models in all evaluation measures.

Nonlinear subspace clustering for image clustering

Functional Link Neural Network (FLNN) has emerged as an important tool for solving classification problems and widely applied in many engineering and scientific problems. FLNN is known to be conveniently used as compared to ordinary feed forward network like the Multilayer Perceptron (MLP) due to its flat network architecture which employs less tuneable weights. The standard method for tuning the weight in FLNN is using a Backpropagation (BP) learning algorithm. However, BP-learning algorithm has difficulties such as trapping in local minima and slow convergence especially for solving non-linearly separable classification problems. In this work, a modified Artificial Bee Colony (mABC) is used to recover the BP drawbacks. With modifications on the employed bee’s exploitation phase, the implementation of the mABC as a learning scheme for FLNN is expected to give a better accuracy result for the classification tasks.

For nonlinear channel distortions of chaos-based communication systems，based on the analysis of the theory of chaotic signal reconstruction and the characteristics of transversal filter and functional link neural network (FLNN)，a novel nonlinear adaptive equalizer with the architecture of combination of transversal filter and functional link neural network (CFFLNN) is proposed in this paper. The novel nonlinear equalizer fully utilizes faster convergence characteristics of transversal filter and the nonlinear approximation capability of FLNN by function expansion due to enhanced input space. Furthermore，the performance of the novel nonlinear adaptive equalizer is also improved. Finally，the proposed equalizer is designed and its adaptive algorithm is deduced by the low complexity normalized least mean square (NLMS) method. And an analysis of stability and convergence for the derived algorithm is provided. To illustrate the analysis，results obtained from the computer simulation are also provided for both linear and nonlinear channels in chaos-based communication system.

The model proposed in this paper, is a hybridization of fuzzy neural network (FNN) and a functional link neural system for currency exchange rate prediction. The TSK-type feedforward fuzzy neural network does not take the full advantage of the use of the fuzzy rule base in accurate input-output mapping and hence a hybrid model is developed using the functional link neural network (FLANN) to construct the consequent part of the fuzzy rules. The FLANN model is used to provide an expanded nonlinear transformation to the input space thereby increasing its dimension which will be adequate to capture the nonlinearities and chaotic variations in the currency exchange time series. Further hybridizing it with Fuzzy neural network will result in a significant accuracy in day ahead currency exchange rate prediction. Currency exchange rates between US Dollar (USD) and other four currencies such as Australian Dollar (AUD), Indian Rupee (INR), Japanese Yen (JPY), and Canadian Dollar (CAD) datasets are used to validate the efficacy of the proposed FLFNN.

In this article, we propose a deep extension of sparse subspace clustering, termed deep subspace clustering with L1-norm (DSC-L1). Regularized by the unit sphere distribution assumption for the learned deep features, DSC-L1 can infer a new data affinity matrix by simultaneously satisfying the sparsity principle of SSC and the nonlinearity given by neural networks. One of the appealing advantages brought by DSC-L1 is that when original real-world data do not meet the class-specific linear subspace distribution assumption, DSC-L1 can employ neural networks to make the assumption valid with its nonlinear transformations. Moreover, we prove that our neural network could sufficiently approximate the minimizer under mild conditions. To the best of our knowledge, this could be one of the first deep-learning-based subspace clustering methods. Extensive experiments are conducted on four real-world data sets to show that the proposed method is significantly superior to 17 existing methods for subspace clustering on handcrafted features and raw data.

As the high growth of the number of vehicles, the traffic accidents are becoming more and more serious in recent years. In order to avoid the drivers being in danger, an intelligent vision-based system should focus on the image contents of the front the camera setting under the rear-view mirror in the vehicle. In this paper, we present a functional-link-based neuro-fuzzy network (FLNFN) structure for lane detection and departure warning system application. The proposed FLNFN model uses a functional link neural network (FLNN) to the consequent part of the fuzzy rules. This study uses orthogonal polynomials and linearly independent functions in a functional expansion of the FLNN. Thus, the consequent part of the proposed FLNFN model is a nonlinear combination of input variables. An online learning algorithm, which consists of structure learning and parameter learning, is also presented. The structure learning depends on the entropy measure to determine the number of fuzzy rules. The parameter learning, based on the gradient descent method, can adjust the shape of the membership function and the corresponding weights of the FLNN. The lane detection method and the departure warning system proposed in this paper have been successfully evaluated on a PC platform of 3.2-GHz CPU, where the average frame-rate is up to 30fps.

This study presents a functional-link-based neuro-fuzzy network (FLNFN) structure for nonlinear system control. The proposed FLNFN model uses a functional link neural network (FLNN) to the consequent part of the fuzzy rules. This study uses orthogonal polynomials and linearly independent functions in a functional expansion of the FLNN. Thus, the consequent part of the proposed FLNFN model is a nonlinear combination of input variables. An online learning algorithm, which consists of structure learning and parameter learning, is also presented. The structure learning depends on the entropy measure to determine the number of fuzzy rules. The parameter learning, based on the gradient descent method, can adjust the shape of the membership function and the corresponding weights of the FLNN. Finally, the FLNFN model is applied in various simulations. Results of this study demonstrate the effectiveness of the proposed FLNFN model.

Recent efforts to incorporate aspects of artificial intelligence into the design and operation of automatic control systems have focused attention on techniques such as fuzzy logic, artificial neural networks and expert systems. The use of computers for direct digital control highlights the recent trend toward more effective and efficient heating, ventilating and air-conditioning (HVAC) control methodologies. Researchers in the HVAC field have stressed the importance of self-learning in building control systems and have encouraged further studies in the integration of optimal control and other advanced techniques into the formulation of such systems. Artificial neural networks can also be used to emulate the plant dynamics, in order to estimate future plant outputs and obtain plant input/output sensitivity information for online neural control adaptation. This paper describes a functional link neural network approach to performing the HVAC thermal dynamic system identification. Methodologies to reduce inputs of the functional link network to reduce the complexity and speed up the training speed are presented. Analysis and comparison between the functional link network approach and the conventional network approach for the HVAC thermal modeling are also presented.

This chapter presents an evolutionary neural fuzzy network, designed using the functional-link-based neural fuzzy network (FLNFN) and a new evolutionary learning algorithm. This new evolutionary learning algorithm is based on a hybrid of cooperative particle swarm optimization and cultural algorithm. It is thus called cultural cooperative particle swarm optimization (CCPSO). The proposed CCPSO method, which uses cooperative behavior among multiple swarms, can increase the global search capacity using the belief space. Cooperative behavior involves a collection of multiple swarms that interact by exchanging information to solve a problem. The belief space is the information repository in which the individuals can store their experiences such that other individuals can learn from them indirectly. The proposed FLNFN model uses functional link neural networks as the consequent part of the fuzzy rules. This chapter uses orthogonal polynomials and linearly independent functions in a functional expansion of the functional link neural networks. The FLNFN model can generate the consequent part of a nonlinear combination of input variables. Finally, the proposed functional-link-based neural fuzzy network with cultural cooperative particle swarm optimization (FLNFN-CCPSO) is adopted in several predictive applications. Experimental results have demonstrated that the proposed CCPSO method performs well in predicting the time series problems.